We study the topological properties of Calabi-Yau threefold hypersurfaces at large h 1,1 . We obtain two million threefolds X by triangulating polytopes from the Kreuzer-Skarke list, including all polytopes with 240 ≤ h 1,1 ≤ 491. We show that the Kähler cone of X is very narrow at large h 1,1 , and as a consequence, control of the α expansion in string compactifications on X is correlated with the presence of ultralight axions. If every effective curve has volume ≥ 1 in string units, then the typical volumes of irreducible effective curves and divisors, and of X itself, scale as (h 1,1 ) p , with 3 p 7 depending on the type of cycle in question. Instantons from branes wrapping these cycles are thus highly suppressed.
Several recent works [1][2][3] have claimed that the Weak Gravity Conjecture (WGC) excludes super-Planckian displacements of axion fields, and hence large-field axion inflation, in the absence of monodromy. We argue that in theories with N 1 axions, super-Planckian axion diameters D are readily allowed by the WGC. We clarify the nontrivial relationship between the kinetic matrix K -unambiguously defined by its form in a Minkowski-reduced basis -and the diameter of the axion fundamental domain, emphasizing that in general the diameter is not solely determined by the eigenvalues f 2 1 ≤ . . . ≤ f 2 N of K: the orientations of the eigenvectors with respect to the identifications imposed by instantons must be incorporated. In particular, even if one were to impose the condition f N < M pl , this would imply neither D < M pl nor D < √ N M pl . We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by S ≥ SM pl /f N , with S a fixed constant, but in the universal limit S S √ N M pl /f N . Thus, having f N > M pl does not immediately imply the existence of unsuppressed higher harmonic contributions to the potential. Finally, we argue that in effective axion-gravity theories, the zero-form version of the WGC can be satisfied by gravitational instantons that make negligible contributions to the potential.
We study universality of geometric gauge sectors in the string landscape in the context of Ftheory compactifications. A finite time construction algorithm is presented for 4 3 × 2.96 × 10 755 Ftheory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with probability above 1 − 1.01 × 10 −755 , and the geometric gauge group rank is above 160 with probability .999995. In the latter case there are at least 10 E8 factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from E6 or SU (3) seven-branes, which occur in certain random samples with probability ≃ 1 200.
We propose a scenario for realizing super-Planckian axion decay constants in Calabi-Yau orientifolds of type IIB string theory, leading to large-field inflation. Our construction is a simple embedding in string theory of the mechanism of Kim, Nilles, and Peloso, in which a large effective decay constant arises from alignment of two smaller decay constants. The key ingredient is gaugino condensation on magnetized or multiply-wound D7-branes. We argue that, under very mild assumptions about the topology of the Calabi-Yau, there are controllable points in moduli space with large effective decay constants.
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